The main goal of this paper is to find the Fisher-Shannon and LMC complexities for the Laguerre and Gegenbauer orthonormal polynomials with an arbitrary fixed degree when the weight function's parameter tends to infinity. This issue is theoretically relevant in the theory of special functions, and because of its direct applications to compute the physical entropies of quasi-classical or high dimensional states of multidimensional systems in quantum physics and quantum tecnologies [1]}, [2]}, [3]}, [4]}; the latter is because the radial and spherical components of the state's wavefunctions are controlled by Laguerre and Gegenbauer polynomials with a parameter which depends on the space dimensionality of the systems, respectively. The Gegenbauer polynomials are well known [5]}, [6]} to be a particular family of the Jacobi polynomials. We will use the recent methodology of Temme et al. [7]}, [2]} which is based on the weight-function's parameter asymptotics of the (unweighted) \(\mathfrak {L}_{q}\) -norms of the HOPs with a fixed degree. It is worth remarking that we do not consider here the complexity-like measures of polynomials with varying weights (i.e., polynomials whose weight-function's parameter does depend on the polynomial degree), which are also of great mathematical and physical interest [9]}, [10]}, [11]}.
